# (435e) Methane Steam Reforming Unraveled By the Microkinetic Engine, a User-Friendly Kinetic Modelling Tool

#### AIChE Annual Meeting

#### 2016

#### 2016 AIChE Annual Meeting

#### Catalysis and Reaction Engineering Division

#### Reaction Path Analysis

#### Tuesday, November 15, 2016 - 4:07pm to 4:20pm

Kinetic

modelling forms the bridge between the phenomena occurring at the molecular and

reactor scale. It results in a mathematical representation of the underlying

reaction mechanisms which ratify or debunk the assumptions made. This turns it

an important activity in chemical engineering because it allows the

optimization and intensification of industrial chemical processes. From an

industrial point of view, global kinetic models such as power law or

Langmuir-Hinshelwood-Hougen-Watson (LHHW) models

often provide sufficient, reliable information for process control and

optimization. However, decreasing margins and increasing computational

capabilities open up perspectives for more fundamental kinetic modelling for

industry which, up to recently, was only exploited by academia. In addition,

the shift towards ‘green’ production processes underlines the need for a more

detailed understanding of the more complex nature of biomass conversion.

Dedicated

software with various features is available to construct such (micro)kinetic

models. However, there is a significant induction period for novices in the

field of kinetic modelling since a good knowledge of chemistry, mathematics,

statistics and (chemo)informatics is required. In order to make fundamental

kinetic modelling more accessible and to reduce the time spent for model

construction, a user-friendly tool has been developed: the MicroKinetic

Engine (µKE).

**MicroKinetic**** Engine (µKE)**

The

µKE is a software package for the simulation and regression of chemical

kinetics and even non-chemical applications such as solar cells. This package

has been developed during the last decade at the Laboratory for Chemical

Technology, Ghent University and was originally constructed for the detailed

kinetic modelling of heterogeneously catalyzed reactions. In order to simulate

different reactor types, both differential and algebraic solvers are integrated

in the software’s library. To enable model regression to experimental data, two

deterministic regression routines are included, i.e., the Rosenbrock

[1] and Levenberg-Marquardt algorithm [2]. A

Graphical User Interface (GUI), see Figure 1 (left), is wrapped around all

these routines such that no programming effort whatsoever is required from the

µKE user, making it very distinct from other chemical modelling tools such as

Athena Visual Studio [3] or Chemkin [4].

**Figure ****1.
Graphical User Interface of the MicroKinetic Engine.
Left: window for problem definitions, right: window for automatic network
generation**

The

µKE consists of an onion structure as indicated in Figure

2. At its core, the µKE has the kinetic model which expresses the

reaction rates of every (elementary) step included in the reaction network. By

default, the law of mass action is applied to describe these reaction rates,

but also power laws or user defined rates can be included. Due to the latter,

also applications other than chemical kinetics can be handled by the µKE, for

example simulating a solar cell’s performance as a function of its properties

and the applied voltage. These rate equations are subsequently incorporated in

a reactor model which describes the mass balance of all components over the

selected reactor type. The corresponding set of algebraic and/or differential equations

is solved using DASPK3.0 [5] in order to calculate the individual outlet flow

rates. If regression is required, an additional shell is activated in which the

Rosenbrock method performs a first estimation effort,

after which the Levenberg-Marquardt algorithm is

called to further optimize the parameter estimates. Both regression algorithms

are based on the minimization of the (weighted) residual sum of squares of the

responses in order to determine optimal parameter estimates.

**Figure ****2. Structure of the MicroKinetic Engine**

The

input of the µKE comprises (initial) parameter values, experimental data,

including independent and dependent variables, and the proposed reaction

network for chemical kinetics. The reaction network can be constructed either

manually via the GUI, or automatically based on the integration with the

Reaction Network Generator (ReNGeP) [6] or, by extension, by any other network

generation program, see Figure 1 (right). The µKE automatically converts the

reaction network into the corresponding rate equations which are subsequently

substituted in the reactor model. Instead of a reaction network, user-defined

equations can be given which are applicable to both chemical and non-chemical

systems. The output of the optimization procedure consists of the model

predictions and, in case of regression, an extended statistical analysis and

the corresponding optimal parameter estimates. In case of reversible steps, the

parameter estimates are determined such that thermodynamic consistency is

assured for each of the reaction steps. Additionally, the µKE identifies

quasi-equilibrated reaction steps while no assumptions have to be made *a
priori* on rate-determining step(s) or quasi-equilibria. If required, a rate

of production analysis is performed by the µKE providing an additional layer of

insight in the reaction network included.

** **

**Methane
steam reforming **

To

demonstrate the features and versatility of the µKE, methane steam reforming is

selected as a case study. To model the reaction mechanism of this industrially

relevant process, a LHHW type kinetic model is proposed. The model is regressed

to the experimental data acquired by Oyama et al.. The dataset comprises 80

experiments, performed in a tubular packed bed reactor at a total pressure of

0.4 MPa in a temperature range from 893 to 943 K with space times ranging from

0.82 to 5.76 kg s mol^{-1} and CH_{4} to H_{2}O molar

ratios between 0.125 and 0.7. In some experiments, CO, CO_{2} and/or H_{2}

were added to the feed. The catalyst is an industrial SiO_{2}-MgO

supported Ni catalyst.

The

reaction network used for the kinetic model is shown in Figure 3. The

adsorption/desorption steps are assumed to be in quasi-equilibrium, without

making *a priori* any other assumptions about the surface reactions. The

weighted regression of this adequate model was found to be globally significant

(F_{cal} = 10325 and F_{tab}

= 2) with statistically significant parameter estimates, see Table 1. The model

showed an acceptable performance combined with a clear physical meaning, see

Figure 4.

** **

**Figure ****3.
Reaction network for the Langmuir-Hinshelwood kinetic model for methane steam
reforming.**

**Figure ****4.
Methane conversion as a function of the water inlet pressure at a total
pressure of 0.4 MPa and a temperature of 923 K. Symbols: experimentally
observed with blue = 40 kPa inlet partial
pressure of CH**

_{4}(p

_{CH4,in}) or a space time of 2.88 kg s mol

^{-1}, red = 80 kPa p

_{CH4,in}or 1.44 kg s mol

^{-1}, green = 120 kPa p

_{CH4,in}or 0.96 kg s mol

^{-1}, full line: simulated via weighted regression.

** **

**Table ****1.
95% confidence interval of the model parameters of the Langmuir-Hinshelwood
model.**

parameter |
95% confidence interval |
units |

K |
5.57 ± 0.74 |
10 |

K |
4.18 ± 0.32 |
10 |

k |
14.50 ± 1.91 |
mol s |

K |
8.26 ± 6.80 |
10 |

k |
9.53 ± 3.00 |
mol s |

K |
4.27 ± 1.51 |
10 |

K |
2.61 ± 0.86 |
10 |

K |
1.24 ± 0.53 |
10 |

K |
6.51 ± 1.70 |
10 |

A

rate of production analysis (RPA) is performed with the µKE, based on the parameter

estimates of the Langmuir-Hinshelwood model. In the selected experiment for the

RPA a mixture containing 120 kPa CH_{4}, 200 kPa H_{2}O and 80 kPa N_{2}

(inert) is fed to the reactor at a temperature of 923 K and a space time of

0.96 kg_{cat} s mol^{-1}, resulting

in a conversion of 30 % and selectivities to CO and CO_{2} equal to 30

and 70% respectively. The visual representation of the RPA at the beginning and

the end of the reactor is shown in Figure 5. Based on the RPA, it is clear that

both at the beginning and the end of the reactor the forward steps are most

dominant as indicated by the differences in arrow thickness in Figure 5.

Throughout the reactor the water-gas shift reaction gains importance.

**Conclusion**

Through

the case study of methane steam reforming, the µKE has proved to be a well

performing and strongly user-friendly software package for the simulation and

regression of chemical kinetics. With minor user intervention, regressions

could be performed providing, in an automated manner, the statistical

interpretation of these results, such that the user can focus on their physical

interpretation. A rate of production analysis was successfully carried out at

two positions in the reactor and indicated the sequence of the steam reforming

followed by the water-gas shift reaction. Additionally, both reactions are

close to being irreversible.

**Figure ****5.
Visual representation of the rate of production analysis of the
Langmuir-Hinshelwood model. Left: forward steps, right: reverse steps, top: at
reactor inlet, bottom, at reactor outlet. Experimental conditions: inlet flow
containing 120 kPa CH**

_{4}, 200 kPa H

_{2}O and 80 kPa N

_{2}at a temperature of 923 K and a space time of 0.96 kg

_{cat}s mol

^{-1}, resulting in a conversion of 30 % and selectivities to CO and CO

_{2}equal to 30 and 70 % respectively.

**References**

[1] H.H. Rosenbrock,

AN AUTOMATIC METHOD FOR FINDING THE GREATEST OR LEAST VALUE OF A FUNCTION, Comput. J., 3 (1960) 175-184.

[2] D.W. Marquardt, AN ALGORITHM

FOR LEAST-SQUARES ESTIMATION OF NONLINEAR PARAMETERS, Journal of the Society

for Industrial and Applied Mathematics, 11 (1963) 431-441.

[3] Athena Visual Studio, http://www.athenavisual.com/.

[4]

Chemkin, http://www.reactiondesign.com/products/chemkin/chemkin-2/.

[5]

S. Li, L. Petzold, DASPK 3.0, https://techtransfer.universityofcalifornia.edu/NCD/10326.html.

[6]

J.W. Thybaut, G.B. Marin, Single-Event MicroKinetics:

Catalyst design for complex reaction networks, J. Catal.,

308 (2013) 352-362.

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